TL;DR Summary

• The phrase “In God We Trust wasn’t always on our money” states the propaganda poster.
• This poster is both true and false, depending on how you define “money”.
• It has been on some coins since 1909, for example.
• The goal of the poster was to argue about separation of state and church (we think). It works due to (a) a true assertion, and (b) “What you see is all there is” and the viewer is not aware that the phrase was on other forms of currency before appearing on the one dollar bill.

The phrase “In God we trust” was affixed to coins starting in the 19th century, during the Civil War. In 1956, Congress passed a law, signed by the President, to place the motto on to paper currency starting in 1957. Thus, that part of the poster is true.
Source: http://www.treasury.gov/about/education/Pages/in-god-we-trust.aspx
But per the Treasury, “The motto has been in continuous use on the one-cent coin since 1909, and on the ten-cent coin since 1916. It also has appeared on all gold coins and silver dollar coins, half-dollar coins, and quarter-dollar coins struck since July 1, 1908.”
The implication of the statement “No, it wasn’t always on our money!” is misleading and is false in implying there was no such statement prior to 1957.
This item was “Shared!” into my FB news feed and had been shared 16,000 times at the time it appeared. As of today, it has been shared 24,000 times. (Source: “Being Liberal”).